According to the Multiple-input Multiple-output (MIMO) communication technology, multiple transmit antennas of a transmitter and multiple receive antennas of a receiver are used for the transmission of a data stream from the transmitter to the receiver. MIMO has been considered in several communication standards in order to achieve a higher throughput. Although open-loop MIMO techniques have already shown to achieve high performance gain, the availability of either full or partial channel state information (CSI) at the transmitter, e.g. a base-station of a mobile communication network, typically leads to additional performance gain and sometimes even complexity reduction. Such closed-loop schemes have been considered in IEEE 802.11n, IEEE 802.16, and 3GPP Long Term Evolution (LTE) for application of beamforming or multi-user precoding.
However, channel state information estimation for the downlink channel at a base-station is not possible in communication systems using FDD (frequency division duplexing), and it is also not straight forward in communication systems using TDD (time division duplexing) due to the mismatch in the radio frequency front end. Hence, the channel state information is typically estimated by the receiving mobile terminal, quantized, and sent back to the base-station. This, unfortunately, requires a high feedback bandwidth. So, the mobile terminal may compute a beamforming vector or matrix, which is usually a unit norm vector or unitary matrix, and compress this vector or matrix before feeding it back to the base-station. By compression and quantization the feedback bandwidth requirement may be greatly reduced.
The feedback bandwidth saving is even more substantial for communication systems employing OFDM (orthogonal frequency division multiplexing). For communication systems according to IEEE 802.11n with 20 MHz bandwidth, 52 data sub carriers are allocated for the transmission of data streams. Then a 4 bits feedback per sub carrier will require 208 bits, a 6 bits feedback per sub carrier will require 312 bits (which is 50% increment over 4 bits case), and a 8 bits feedback per sub carrier will require 416 bits (which is 100% increment over 4 bits case). To feedback a few hundreds of bits in a timely manner to a base-station will pose a challenging task, hence a low complexity scheme that can provide good performance at low feedback rate is highly desirable.